In this paper we study a two-dimensional system of charged colloidal particles using Brownian dynamics simulations. We determine the phase diagram and investigate the dynamics of this system in the density regime where hexatic and solid phases are stable. We find that the dynamics in these phases is heterogeneous by means of the spontaneous formation and diffusion of highly mobile defects. We identify two key mechanisms associated with the areas of high mobility. The first mechanism involves the highly cooperative motion of a closed loop of particles which shift coherently along the loop until each particle has replaced the position of its predecessor in the chain. The second mechanism involves the spontaneous creation of vacancy-interstitial pairs which diffuse within the hexatic and solid phases. We further explore quantitatively the properties of the open-ended and closed rearrangement strings and find that in the crystal phase the string-size distribution can be approximately matched with a simple, random walk description of vacancies and interstitials on a lattice.